Description Usage Arguments Details Value See Also

Infers the problem type and learns the appropriate kernel model.

1 2 3 |

`K` |
n-by-n matrix of pairwise kernel values over a set of n samples |

`y` |
n-by-1 vector of response values. Must be numeric vector for regression, factor with 2 levels for binary classification, or NULL for a one-class task. |

`lambda` |
scalar, regularization parameter |

`a` |
n-by-1 vector of sample weights (regression only) |

`max.iter` |
maximum number of iterations (binary classification and one-class problems only) |

`eps` |
convergence precision (binary classification and one-class problems only) |

`v.init` |
initial parameter estimate for the kernel weights (binary classification and one-class problems only) |

`b.init` |
initial parameter estimate for the bias term (binary classification only) |

`fix.bias` |
set to TRUE to prevent the bias term from being updated (regression only) (default: FALSE) |

`silent` |
set to TRUE to suppress run-time output to stdout (default: FALSE) |

`balanced` |
boolean specifying whether the balanced model is being trained (binary classification only) (default: FALSE) |

The entries in the kernel matrix K can be interpreted as dot products
in some feature space *φ*. The corresponding weight vector can be
retrieved via *w = ∑_i v_i φ(x_i)*. However, new samples can be
classified without explicit access to the underlying feature space:

*w^T φ(x) + b = ∑_i v_i φ^T (x_i) φ(x) + b = ∑_i v_i K( x_i, x ) + b*

The method determines the problem type from the labels argument y. If y is a numeric vector, then a ridge regression model is trained by optimizing the following objective function:

* \frac{1}{2n} ∑_i a_i (z_i - (w^T x_i + b))^2 + w^Tw *

If y is a factor with two levels, then the function returns a binary classification model, obtained by optimizing the following objective function:

* -\frac{1}{n} ∑_i y_i s_i - \log( 1 + \exp(s_i) ) + w^Tw *

where

* s_i = w^T x_i + b *

Finally, if no labels are provided (y == NULL), then a one-class model is constructed using the following objective function:

* -\frac{1}{n} ∑_i s_i - \log( 1 + \exp(s_i) ) + w^Tw *

where

* s_i = w^T x_i *

In all cases, *w = ∑_i v_i φ(x_i)* and the method solves for *v_i*.

A list with two elements:

- v
n-by-1 vector of kernel weights

- b
scalar, bias term for the linear model (omitted for one-class models)

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